RMS RESPONSE OF A ONE-DIMENSIONAL HALF-SPACE TO SH

We examine the extent to which the response of a perfectly elastic hal fspace to an SH-wave incident from below can be characterized when kno wledge about the elastic structure is Limited to the near surface. Ela stic properties are modeled as piecewise continuous functions of the d epth coordinate. It is found that the site amplification function can be determined with a frequency resolution that depends inversely on th e depth to which the elastic structure is known. Specifically, certain spectral averages of the site amplification function, concentrated ov er bandwidth Delta f, depend only on the elastic structure down to a t wo-way travel-time depth of 1/Delta f. These spectral averages are ent irely independent of the elastic properties at greater depth. Equivale ntly, when the incident motion has a bandlimited white power spectrum of bandwidth Delta f, the site amplification of the root mean square ( rms) ground motion depends only on the elastic structure down to a two -way travel-time depth of 1/Delta f. When the bandwidth is sufficientl y large, the following corollary applies: the rms surface ground motio n equals the rms incident motion multiplied by 2 root I-b/I-0, where I -0 and I-b are shear impedances at the ground surface and basement dep th, respectively. This result provides justification for a procedure c onventionally used to correct stochastic estimates of earthquake groun d motion to account for local site effects. The analysis also clarifie s the limitations of that conventional procedure. The results define s pecific site-response parameters that can be computed from knowledge o f shallow structure alone and may thereby contribute to improved under standing of the physical basis for, and limitations of, site classific ation schemes that are based on average S-wave velocity at shallow dep th. While the analytical results are rigorous only for infinite Q, num erical experiments indicate that similar results apply to models with finite, frequency-independent Q. The practical utility of the results is likely to be limited primarily by the degree of lateral heterogenei ty present near sites of interest and the degree to which the sites re spond nonlinearly to incident ground motion.